Finite Group Databasebeta

← #15793009

Subgroups — #15793009

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718892C211yesmaximal, characteristic
2C2×#11718891C211yesmaximal, characteristic, complemented
3C2×#11718329C211yesmaximal, characteristic
4C2×#11718650C211yesmaximal, characteristic
5#13113100C211yesmaximal, characteristic, complemented
6#13113099C211yesmaximal, characteristic, complemented
7#13113094C211yesmaximal, characteristic, complemented
8#13113091C211yesmaximal, characteristic, complemented
9#13113080C211yesmaximal, characteristic
10#13113074C211yesmaximal, characteristic
11#13113072C211yesmaximal, characteristic
12#13113063C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C2×C13×#391C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#391—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36#11718892C418yescomplemented
37#11718891—24no—
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718650—24no—
55#11718329—24no—
56C24×D13C2311yescharacteristic
57C22×Q8×C13—22no—
58C22×Q8×C13—22no—
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—41no—
62C22×Q8×C13—41no—
63C22×Q8×C13C2×C414yescomplemented
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C22×C4×D13—22no—
79C22×C4×D13—22no—
80C22×C4×D13—22no—
81C22×C4×D13—41no—
82C22×C4×D13—41no—
83C22×C4×D13—41no—
84C22×C4×D13—41no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—41no—
88C2×C42×C13—22no—
89C2×C42×C13—22no—
90C2×C42×C13—41no—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—41no—
100C2×#6103—41no—
101C2×#6103—41no—
102C2×#6103—41no—
103C2×#6103—41no—
104C2×#6103—41no—
105C2×#6103C2×C414yes—
106C2×#6103C2×C414yes—
107C2×#6103C2×C414yes—
108C2×#6103Q814yescomplemented
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—41no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—41no—
115C2×#6101—41no—
116C2×#6101—41no—
117C2×#6101—41no—
118C2×#6101—41no—
119C2×#6101—41no—
120C2×#6101—41no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—41no—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95D414yes—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071C2×C414yescomplemented
141#88071C2×C414yescomplemented
142#88071C2×C414yescomplemented
143#88071D414yes—
144#14575—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C2×Q812yes—
160C23×D13#4112yes—
161C2×Q8×C13—28no—
162C2×Q8×C13—28no—
163C2×Q8×C13—44no—
164C2×Q8×C13—44no—
165C2×Q8×C13—44no—
166C2×Q8×C13—44no—
167C2×Q8×C13—44no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13C22×C412yes—
208C22×C4×C13C22×C412yes—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×Q812yes—
215C22×C4×C13#4112yes—
216C22×C4×C13#4112yes—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C22×C412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×Q812yes—
266C2×C4×D13—44no—
267C2×C4×D13—44no—
268C2×C4×D13—44no—
269C2×C4×D13—44no—
270C2×C4×D13—44no—
271C2×C4×D13—44no—
272C2×C4×D13—44no—
273C13×C4⋊C4—44no—
274C42×C13—44no—
275#6103—28no—
276#6103—28no—
277#6103—44no—
278#6103—44no—
279#6103—44no—
280#6103—44no—
281C4⋊Dic13—44no—
282#6101—44no—
283#6101—44no—
284#6101—44no—
285C4×Dic13—44no—
286C2×#393—131no—
287C2×#391—131no—
288C2×#391D1311yescharacteristic, complemented
289C2×#385—131no—
290C2×#385—131no—
291#1444—131no—
292#1444—131no—
293#1442—131no—
294#1442—131no—
295#1439—131no—
296#1437—131no—
297#1437—131no—
298#1434—131no—
299#1434—131no—
300C22⋊#95—131no—
301C23×C13C23×C411yescharacteristic
302C23×C13C22×D411yescharacteristic
303C23×C13C22×D411yescharacteristic
304C23×C13C22×Q811yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C13H(5,𝔽2)11yescharacteristic
312C23×C13H(5,𝔽2)11yescharacteristic
313C23×C132−1+411yescharacteristic
314C23×C132−1+411yescharacteristic
315C23×C132−1+411yescharacteristic
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13—41no—
347C22×D13—41no—
348C22×D13—41no—
349C22×D13—41no—
350C22×D13C4×Q814yes—
351Q8×C13—416no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13C4×D414yes—
400C2×C4×C13C4×D414yes—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C4×D13—416no—
451C23×Q8C2×D1311yescharacteristic
452C24×C4—131no—
453C22×C4⋊C4—131no—
454C22×C4⋊C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4C2×D1311yescharacteristic
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C22⋊C4—131no—
461C22×C22⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C42—131no—
465C22×C42C2×D1311yescharacteristic
466#393—138no—
467#391—24no—
468#391—264no—
469#385—264no—
470#385—264no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95C2×D1311yescharacteristic
488C2×#95C2×D1311yescharacteristic
489C2×#95C2×D1311yescharacteristic
490C2×#95C2×D1311yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C2×C4×Q811yescharacteristic
494C22×C13#51811yescharacteristic
495C22×C13#52011yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13#52011yescharacteristic
498C22×C13#53511yescharacteristic
499C22×C13#53511yescharacteristic
500C22×C13#53611yescharacteristic
501C22×C13#53611yescharacteristic
502C22×C13#53811yescharacteristic
503C22×C13#53911yescharacteristic
504C22×C13#54211yescharacteristic
505C22×C13#54211yescharacteristic
506C22×C13#54211yescharacteristic
507C22×C13#54211yescharacteristic
508C22×C13#54311yescharacteristic
509C22×C13#54411yescharacteristic
510C22×C13D4211yescharacteristic
511C22×C13#54611yescharacteristic
512C22×C13#54611yescharacteristic
513C22×C13#54611yescharacteristic
514C22×C13#54611yescharacteristic
515C22×C13D4×Q811yescharacteristic
516C22×C13D4×Q811yescharacteristic
517C22×C13#55111yescharacteristic
518C22×C13#55211yescharacteristic
519C22×C13#55211yescharacteristic
520C22×C13#55411yescharacteristic
521C22×C13#55411yescharacteristic
522C22×C13H(3,𝔽4)11yescharacteristic
523C22×C13#56211yescharacteristic
524C22×C13#56211yescharacteristic
525C22×C13#56311yescharacteristic
526C2×D13—24no—
527C2×D13—24no—
528C2×D13—24no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C2×D13—42no—
537C2×D13—42no—
538C2×D13—42no—
539C2×D13—42no—
540C2×D13—42no—
541C4×C13—24no—
542C4×C13—24no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—81no—
548Dic13—42no—
549Dic13—42no—
550Dic13—42no—
551Dic13—42no—
552Dic13—42no—
553Dic13—42no—
554Dic13—81no—
555C25—131no—
556C22×Q8—22no—
557C22×Q8—22no—
558C22×Q8—22no—
559C22×Q8—22no—
560C22×Q8—41no—
561C22×Q8—41no—
562C22×Q8C4×D1314yescomplemented
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—262no—
571C23×C4—262no—
572C23×C4—262no—
573C23×C4—521no—
574C23×C4—521no—
575C23×C4—521no—
576C23×C4—521no—
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C23×C4C22×D1311yescharacteristic
583C23×C4C22×D1311yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—521no—
592C2×C4⋊C4—521no—
593C2×C4⋊C4—521no—
594C2×C4⋊C4—521no—
595C2×C4⋊C4—521no—
596C2×C4⋊C4—521no—
597C2×C4⋊C4—521no—
598C2×C4⋊C4—521no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—262no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—262no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4—521no—
614C2×C22⋊C4—521no—
615C2×C22⋊C4—521no—
616C2×C22⋊C4—521no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—41no—
620C2×C42—262no—
621C2×C42—262no—
622C2×C42—521no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—134no—
627#95—134no—
628#95—134no—
629#95—134no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—521no—
636#95—521no—
637#95—521no—
638#95—521no—
639#95—521no—
640#95—521no—
641#95—521no—
642#95C22⋊D1314yes—
643C2×C13#232611yescharacteristic
644C2×C13#232611yescharacteristic
645C2×C13#232911yescharacteristic
646C2×C13#235811yescharacteristic
647C2×C13#236011yescharacteristic
648C2×C13#236011yescharacteristic
649C2×C13#237911yescharacteristic
650C2×C13#267011yescharacteristic
651C2×C13#267711yescharacteristic
652C2×C13#268711yescharacteristic
653C2×C13#268711yescharacteristic
654C2×C13#269211yescharacteristic
655C2×C13#269211yescharacteristic
656C2×C13#276311yescharacteristic
657C2×C13#276411yescharacteristic
658D13—44no—
659C24—132no—
660C24—132no—
661C24—132no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24—261no—
670C24—261no—
671C24—261no—
672C24—261no—
673C24—261no—
674C24C23×D1311yescharacteristic
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—524no—
771C22×C4—524no—
772C22×C4—524no—
773C22×C4—524no—
774C22×C4—524no—
775C22×C4—524no—
776C22×C4—524no—
777C22×C4C2×C4×D1312yes—
778C22×C4C2×C4×D1312yes—
779C22×C4C2×C4×D1312yes—
780C22×C4#612712yes—
781C22×C4D4×D1312yes—
782C22×C4#612912yes—
783C22×C4Q8×D1312yes—
784C22×C4C2×C22⋊D1312yes—
785C22×C4C2×C22⋊D1312yes—
786C22×C4C2×C22⋊D1312yes—
787C4⋊C4—44no—
788C4⋊C4—524no—
789C4⋊C4—524no—
790C4⋊C4—524no—
791C4⋊C4—524no—
792C22⋊C4—268no—
793C22⋊C4—268no—
794C22⋊C4—524no—
795C22⋊C4—524no—
796C22⋊C4—524no—
797C22⋊C4—524no—
798C42—44no—
799C42—524no—
800C13#1457511yescharacteristic, complemented, Sylow
801C23—134no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—262no—
812C23—262no—
813C23—262no—
814C23—262no—
815C23—262no—
816C23—262no—
817C23—262no—
818C23—262no—
819C23—262no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23—521no—
828C23—521no—
829C23—521no—
830C23—521no—
831C23—521no—
832C23—521no—
833C23—521no—
834C23—521no—
835C23—521no—
836C23C22×C4×D1311yescharacteristic
837C23C2×#612711yescharacteristic
838C23C2×D4×D1311yescharacteristic
839C23C2×#612911yescharacteristic
840C23#8825111yescharacteristic
841C23#8825111yescharacteristic
842C23C2×Q8×D1311yescharacteristic
843C23#8825411yescharacteristic
844C23#8825411yescharacteristic
845C23#8825411yescharacteristic
846C23#41×D1311yescharacteristic
847C23#8825611yescharacteristic
848C23#8825611yescharacteristic
849C23#8825611yescharacteristic
850C23C22×C22⋊D1311yescharacteristic
851Q8—416no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—5216no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4#8813514yes—
950C2×C4C4×C22⋊D1314yes—
951C22—264no—
952C22—264no—
953C22—264no—
954C22—522no—
955C22—522no—
956C22—522no—
957C22—522no—
958C22—522no—
959C22—522no—
960C22—522no—
961C22—522no—
962C22—522no—
963C22—522no—
964C22—522no—
965C22—522no—
966C22C2×#8813511yescharacteristic
967C22#1171919111yescharacteristic
968C22#1171919511yescharacteristic
969C22#1171920011yescharacteristic
970C22C4×Q8×D1311yescharacteristic
971C22#1171927911yescharacteristic
972C22#1171927911yescharacteristic
973C22#1171927911yescharacteristic
974C22#1171928411yescharacteristic
975C22#1171928611yescharacteristic
976C22#1171928711yescharacteristic
977C22#1171928711yescharacteristic
978C22#1171933911yescharacteristic
979C22#1171934011yescharacteristic
980C22#1171934311yescharacteristic
981C22#1171934411yescharacteristic
982C22#1171934811yescharacteristic
983C22#1171934811yescharacteristic
984C22#1171935211yescharacteristic
985C22#1171935211yescharacteristic
986C22#1171937911yescharacteristic
987C22#1171938111yescharacteristic
988C22#1171938311yescharacteristic
989C22#1171938811yescharacteristic
990C22#1171942911yescharacteristic
991C22#1171943211yescharacteristic
992C22#1171943411yescharacteristic
993C22#1171944011yescharacteristic
994C22C2×C4×C22⋊D1311yescharacteristic
995C22D4×C22⋊D1311yescharacteristic
996C22#1171951111yescharacteristic
997C22Q8×C22⋊D1311yescharacteristic
998C22#1171952111yescharacteristic
999C22#1171953411yescharacteristic
1000C22#1171953511yescharacteristic
1001C4—24no—
1002C4—24no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—81no—
1008C4—522no—
1009C4—522no—
1010C4—522no—
1011C4—522no—
1012C4—522no—
1013C4—522no—
1014C4—1041no—
1015C2—524no—
1016C2#1311754311yescharacteristic
1017C2#1311755011yescharacteristic
1018C2#1311756811yescharacteristic
1019C2#1311781511yescharacteristic
1020C2#1311783711yescharacteristic
1021C2#1311784611yescharacteristic
1022C2#1311800811yescharacteristic
1023C2#1312105711yescharacteristic
1024C2#1312114611yescharacteristic
1025C2#1312125211yescharacteristic
1026C2#1312125311yescharacteristic
1027C2#1312132711yescharacteristic
1028C2#1312132811yescharacteristic
1029C2#1312224711yescharacteristic
1030C2#1312225611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#391D13
hypocenterC13#14575
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#11718891C2semidirect
5. #13113100C2semidirect
6. #13113099C2semidirect
7. #13113094C2semidirect
8. #13113091C2semidirect
12. #13113063C2semidirect
13. #13113061C2semidirect
15. C2×C13×#391C2semidirect
36. #11718892C4semidirect
63. C22×Q8×C13C2×C4semidirect
108. C2×#6103Q8semidirect
140. #88071C2×C4semidirect
141. #88071C2×C4semidirect
142. #88071C2×C4semidirect
288. C2×#391D13semidirect
562. C22×Q8C4×D13semidirect
800. C13#14575semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117188922
C2×#117188912
C2×#117183292
C2×#117186502
#131131002
#131130992
#131130942
#131130912
#131130802
#131130742
#131130722
#131130632
#131130612
#131130572
C2×C13×#3912
#1457513